Math511Exam2Solutions

2 6 3 1 1 1 64 36 9 41 2 6 3 2 so 2

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Unformatted text preview: X is M(t) = Solution: M (t ) = 0.3 + 0.1e2 t + 0.6 4 t Name ________________________ March 7, 2013 3. A box contains 12 prizes. Six are worth $8, two are worth $6 and four are worth $3. A contestant chooses one of the prizes at random. Let X denote the value of the selected prize. 2 Determine the mean and variance of X. µ = 6 σ = 5 (Reduce each value to an integer.) Solution: P ( X = 8) = 1 2 , P ( X = 6 ) = 1 6 , and P ( X = 3) = 1 3 . So, E ( X ) = E(X2 ) = 1 1 1 × 8 + × 6 + × 3 = 6. 2 6 3 1 1 1 × 64 + × 36 + × 9 = 41. 2 6 3 2 So, σ 2 = E X 2 − E ( X ) = 41 − 36 = 5. () 4. A certain booklet has an av...
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